Surface and bulk properties of ballistic deposition models with bond breaking

Abstract

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability $p$. These systems present a crossover, for small values of $p$, from random to correlated (KPZ) growth of surface roughness, which is studied through scaling arguments and Monte Carlo simulations on one- and two-dimensional substrates. We show that the crossover characteristic time $t_{\times }$ scales with $p$ according to $t_{\times }\sim p^{-y}$ with $y=(n+1)$ and that the interface width at saturation $W_{sat}$ scales as $W_{sat}\sim p^{-\delta }$ with $\delta =(n+1)/2$, where $n$ is either the maximal number of broken bonds or of dislodged suspended particles. This result shows that the sets of exponents $y=1$ and $\delta =1/2$ or $y=2$ and $\delta =1$ found in all previous works focusing on systems with this same type of crossover are not universal. Using scaling arguments, we show that the bulk porosity $P$ of the deposits scales as $P\sim p^{y-\delta }$ for small values of $p$. This general scaling relation is confirmed by our numerical simulations and explains previous results present in literature.

arXiv comment7 pages, 4 figures, 2 tables

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• Dimensional crossover in Kardar-Parisi-Zhang growth